I live in Japan, which shares a lot of cultural artifacts with Korea. Also shares a similar climate and similar crowding.

There was a similar tradition in Japan about leaving the fan on all night here some thirty years ago, although what I remember had mostly to do with catching a cold from it, if you took the time to really understand what the people were saying.

The timer is there for several reasons, the primary one being that people who don't want the fun running all night don't want to have to set an alarm clock so they can shut it off.

Why should they want the fan to not run all night?

Saving electricity is one good reason.

Not wanting to dry the sinuses out is another.

Messing with the body temperature while the body is partially inactive is another.

Not so much now, but electrical insulation 60 years ago was not reliable, and fans left running all night were known to sometimes cause house fires. (And when your neighbor's house is as close as it tends to be in Japan and Korea, a house fire is a community problem, not just an individual problem.)

Translation issues in some cases did cause foreigners whose Japanese skills didn't match their imagination to misinterpret the reasons stated. Not saying that there weren't any strange superstitions involved. There was some of that, too. But there were translation problems as well and I have heard some really strange things from time to time that I've now traced to (mostly) mistranslation.

The sensations felt when you sleep under a fan too long, especially a steady, non-oscillating fan, can be remarkably like what the wikipedia article describes.

The sinuses drying can feel suffocating. The motion of the air, also, can interrupt the breathing rhythm. Both of these things can be a contributing factor in death for elderly or invalid people.

A vent fan pushing kitchen air outside can cause issues with air pressure inside, and, again, can aggravate other issues and become a partial cause of death. Depends on the construction of the building and the health of the occupants, of course.

And the body does partially lose its ability to regulate its temperature during sleep. A constant breeze can screw up temperature regulation as well, and the combination can give a person serious chills on a hot day. (I've felt those chills.) Again, this can combine with other problems and cause death.

So, yeah, the mass media is trying to sell advertisements with alarmist reporting, taking a core of reality and stretching it beyond all belief.

But I'm going to assume that the people who really believe the weird theories are among the fringe, which every country has its share of. Oh, and the foreigners whose Korean language skills don't help them distinguish between primary and contributing causes in reports.